# Can Quantum Field Theory not handle accelerated frames of reference?

Since Quantum Field Theory can't handle gravity, and gravity is mathematically equivalent to acceleration (equivalence principle), does this mean Quantum Field theory can't handle accelerated frames of reference?

• hint: check the Unruh effect. Commented Oct 13, 2021 at 12:04
• "Can't handle" is a pretty loose phrase. We don't know how to quantize gravitational theories without issue, i.e. understand quantum fluctuations of gravitational fields. But that's a whole different issue than dealing with accelerated motion. Commented Oct 13, 2021 at 12:05
• I don't see why this question got down votes. It's a perfectly reasonable question. The whole point of the site is to address misconceptions and confusion about physics and I'd be surprised if the OP is the only person with this issue. Commented Oct 13, 2021 at 13:36
• You seem to think that special relativity deals with frames that don't accelerate and GR deals with frames which accelerate. Look up Rindler coordinates, for example, to see that this is not how it works.
– Tom
Commented Oct 14, 2021 at 20:15

No, quantum field theory is perfectly capable of handling accelerated frames of reference:

1. Quantum Field Theory is based on special relativity. Contrary to some somewhat widespread belief, special relativity is perfectly capable of handling accelerated frames. As long as the spacetime is flat, special relativity is perfectly fine. And the curvature of spacetime doesn't depend on the frame of reference (it is a tensor, a geometric object). This is why you will often hear that the twin paradox can be solved with special relativity alone. The twin on the rocket is on an accelerated frame. But as long as they don't pass near a black hole or something like that, spacetime is flat and special relativity applies.

I understand your confusion, gravity is locally equivalent to acceleration. "Locally" is the important word. This means that in the presence of a gravitational field, for every point of spacetime, you can always choose a frame of reference where in the neighborhood of that point, you are in free fall (i.e. spacetime looks flat, the frame of reference is inertial). But there is no frame of reference such that spacetime looks flat everywhere. The crucial difference between being in an accelerating frame in flat spacetime versus being in a gravitational field is that in the former case there is a global inertial reference frame, where spacetime looks flat everywhere, not just in the neighborhood of some point.

So the difference between special and general relativity isn't that one treats acceleration and the other doesn't, but that one treats flat spacetime and the other treats curved spacetime.

1. Quantum field theory is also capable of handling curved spacetime. Some things must be modified to make it work, but there aren't great issues as long as the spacetime is treated classically. A quantum field in a curved (static or time dependent) classical spacetime works well.

Problems arise when you try to quantize gravity, i.e. treat it as a quantum field. A quantum field theory of gravity. That's what we have not been able to do.

• You might want to note that we can quantize gravity, but not in a renormalizable manner (you get an effective field theory). Commented Oct 15, 2021 at 16:11

Gravity is not "mathematically equivalent to acceleration" - otherwise how could things be accelerated in theories without gravity? Physical principles like the different versions of the equivalence principle need to be stated carefully precisely to avoid issues like this that ultimately arise from sloppy phrasing.

When people say that quantum field theory cannot "handle gravity", they mean that a field theory with the spacetime metric as a dynamical field - as in the Einstein-Hilbert action of general relativity - is not renormalizable. See this question and its answers for more on the incompatibility between general relativity and quantum field theory.

Although it does not have renormalizable theories of gravity, quantum field theory does have specific predictions about what happens to accelerated observers, namely they will see radiation generated through the Unruh effect.